Analysis of free vibration in thin-walled plates using an enhanced polygonal plate element with selective interpolation approach

A highly efficient selective element-interior interpolation approach is proposed that impressively enhances the performance of a spatially isotropic polygonal element (SI-ARS-Poly) and provides outstanding solutions in the displacement and energy norms for the static analysis of thin-walled plate structures (Nguyen and Phan (2023) [22]). In this approach, the element-edge rotations and shear strains are respectively interpolated into interior of polygonal element using linear and quadratic approximations. In order to comprehensively explore the advantages of this element, we extend it to free vibration analysis. Numerical results demonstrate that the proposed approach is stable in the free vibration analysis of plates with smoothed mode shapes. Notably, its solutions for free vibration remain robust in the face of mesh distortion. In comparison with other existing polygonal elements, it is superior with the lowest frequencies closely approximate to the exact/reference ones.